دانلود کتاب Hyperidentities and Clones (Algebra, Logic and Applications Series Volume 14)

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Cover
Half Title
Title Page
Copyright Page
Contents
Introduction
1 Basic Concepts
1.1 Algebras
1.2 Compatible relations of an algebra
1.3 Lattices
1.4 Varieties
2 Hyperidentities and Hypervarieties
2.1 Hypersubstitutions and hyperidentities
2.2 Hyperequational classes
2.3 Hyperequational logic
2.4 Hypervarieties
2.5 The clone of a variety
2.6 Hypervarieties o f type T
2.7 The lattice of all solid varieties of type T
2.8 Free clones and solidifyable varieties
2.9 Hypervarieties and bi-identities
3 Hyperidentities in Varieties of Semigroups
3.1 Basic Concepts
3.2 Hyperassociative varieties of semigroups
3.3 Solid varieties of semigroups
3.4 Other types o f algebras
4 M-Hyperidentities and M-Solid Varieties
4.1 Monoids of hypersubstitutions
4.2 Conjugate pairs of additive closure operators
4.3 The lattices of M-solid varieties
4.4 V-proper hypersubstitutions and normal forms
4.5 Exam ples of m onoids of hypersubstitutions
4.6 Subvarieties and subm onoids
4.7 Relations on monoids of hypersubstitutions
4.8 Derived varieties and equational theories
4.9 Hyperquasi-identities and M-solid quasivarieties
4.10 M-solid pseudovarieties
5 M-Solid Varieties of Semigroups
5.1 Pre-solid varieties of semigroups
5.2 Edge-solid varieties of sem igroups
5.3 Regular-solid and dual-solid varieties
5.4 Maps between M-solid varieties of semigroups
5.5 Algorithm ic problems
5.6 Pre-solid and solid varieties of type T = (n)
6 Describing Clones by Hyperidentities
6.1 Basic ideas
6.2 The lattice of all clones on a finite set
6.3 The lattice of all Boolean clones
6.4 Characterizing hyperidentities
6.5 Separation o f clones by hyperidentities
6.6 Separating hyperidentities for Booleanclones
6.7 Varieties generated by Boolean clones
6.8 Projection clones
6.9 Maximal clones and functional completeness
7 Hyperidentities in Partial Algebras
7.1 Terms and identities for partial algebras
7.2 Hypersubstitutions of type T
7.3 Regular hypersubstitutions
7.4 The closure operators XEM and XAM
7.5 Characterization of primal partialalgebras
8 Exercises and Problems
8.1 Exercises
8.2 Problems
Bibliography
Index